A worn out tree (5)
I believe the answer is:
rowan
'tree' is the definition.
(type of tree)
'a worn out' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'a'+'worn'='aworn'
'aworn' with letters rearranged gives 'ROWAN'.
(Other definitions for rowan that I've seen before include "Mr Atkinson, actor" , "-- Williams, theologian" , "Red-berried tree" , "Sort of ash" , "Mountain-ash" .)